Answer:
Part A
The rational equation that can be used to determine how long it would take Lara to clean the tank alone is; 6/9 + 6/x = 1
Part B
It would take Lara 18 hours to clean the tank if she works by herself
Step-by-step explanation:
Part A
The time it takes Kevin to clean an aquarium tank alone = 9 hours
The time it takes Kevin and Lara to clean the tank together = 6 hours
Let '1/x' represent Lara's cleaning rate, we have;
The time it would take Lara to clean 1 tank alone = 1/(1/x) = x
Kevin's cleaning rate, y = 1/9 tank per hour
The number of tanks, z = tank
The total time it takes both of them to clean the tank, t = 6 hours
Therefore, we get;
t × y + t × 1/x = z
When t = 6, y = 1/9, and z = 1, we get;
6 × (1/9) + 6·(1/x) = 1
Therefore, the rational equation that can be used to determine how long it would take Lara to clean the tank if she work by herself, '1/x', is given as follows;
6/9 + 6·(1/x) = 1
6/9 + 6/x = 1
Part B
Solving the rational equation gives;
1/x = (1 - 6/9)/6 = 1/18
∴ 1/x = 1/18)
∴ x = 18
The time it would take Lara to clean the tank if she worked by herself, x = 18 hours
Find the area using sine rules.
Answer:
22.44 mi²Step-by-step explanation:
Step 1
Find the missing angle:
m∠H = 180° - (47° + 99°) = 34°Step 2
Find the missing sides by using the law of sines:
sin 34° / 5.9 = sin 47° / HP = sin 99° / HKHP = 5.9 sin 47°/sin 34° = 7.7 miHK = 5.9 sin 99° / sin 34° = 10.4 miStep 3
Use Heron's formula for the area:
A = [tex]\sqrt{s(s - a)(s - b)(s - c)}[/tex], where s is semi-perimeter, and a, b, c - sidesFind s:
s = 1/2(5.9 + 7.7 + 10.4) = 12Find A:
A = [tex]\sqrt{12(12 - 5.9)(12 - 7.7)( 12 - 10.4)}[/tex] = 22.44 mi²I’ll mark brainliest
Complete the statment with the best choice
All trapezoids are also
_________________.
a. squares b. parallelogram c. rectangles d. quadrilaterals
Answer:
d
Step-by-step explanation:
Help me with this!!!!
Well the half point of 427 and 428 is 427.5 so 427.5.
which equation is written in standard form ?
a. y-3 = -5(x+2)
b. y= 1/2x + 2
c. 3x + 2 = y
d. -7x + 2y = 9
B is standard form. y=1/2x + 2
Answer:
d.-7x+2y=9 that is the answer
Pls help me and thank you!
Line segment AB has endpoints A(0, 3) and B(2, 2). What is the midpoint of
line segment AB?
what is 5 5/7 x 3 1/5?
Zair has 48 marbles in his pocket. He has 3 more blues than the
yellow ones, and 4 times as many yellows as the red ones. How
many of each colored marble is there?
Answer:
# yellow = 20
# blue = 23
# red = 5
Step-by-step explanation:
let 'r' = # red marbles
let '4r' = # yellow marbles
let '3+4r' = # blue marbles
r + 4r + 3 + 4r = 48
9r + 3 = 48
9r = 45
r = 5
red = 5
yellow = 4(5) = 20
blue = 3+4(5) = 23
Which of the following coordinate pairs make the equation x - 9y = 12 true?
(12, 0)
(0, 12)
(3, -1)
(0, -4/3)
Answer:
first one............
Is this correct ? What’s the answer??
Answer:
Im not sure Im sorry Im just trying to get points but I will send to a friend to help
Step-by-step explanation:
Helppppp i need help ASAP
Answer:
a) 10.10 a.m. , (b) 10.20 a.m. which is 10 minutes after sprints start , (c) The students work at 10.50 a.m. , (d) For 60 minutes from 10 a.m. to 11 a.m. which equals to 1 hour
A man's income is increased in the ratio 47:40.find the increase percentage
Answer:
14.8%
Step-by-step explanation:
Given data
Initial income=47
Final income=40
The change= 47-40
=7
Hence the percent increase is
% increase= Change/ initial*100
% increase= 7/47*100
% increase=0.148*100
% increase=14.8%
At a really nice
restaurant, Seiji
wanted to leave a
20% tip for the
outstanding waiter.
The bill was $75.64.
SHOW WORK!!!
Answer:
tip = $15.128
Step-by-step explanation:
tip = 75.64 × 20/100
tip = 1512.8/100
tip = $15.128
I’ll give points but please help me on this and if you don’t know the answer please don’t answer the question thank you
Every time Vince orders Chinese food, he gets egg drop soup. So, he decides to learn how to make it himself. His recipe calls for 1.5 liters of broth, but he can only find 500-milliliter cartons at the store. How many cartons should he buy?
Answer: 3
Step-by-step explanation:
Vince will have to buy three cartons of 500 ml each.
What is expression in mathematics?An expression in mathematics is a combination of terms both constants and variables.
Given is that every time Vince orders Chinese food, he gets egg drop soup. So, he decides to learn how to make it himself. His recipe calls for 1.5 liters of broth, but he can only find 500 milliliter cartons at the store.
We know that -
1 Liter = 1000 milliliters
1.5 liter = 1500 liters
Now -
1 carton 500 ml.
Then, 1 ml will be in (1/500) carton.
So, 1500 ml will be in (1/500 x 1500) = 3 cartons
Therefore, Vince will have to buy three cartons of 500 ml each.
To solve more questions on algebraic expressions, visit the link below -
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This is a sketch of the curve with equation y = f(x).
The vertex of the curve is at (2, -3)
V
X
(2, -3)
Write down the coordinates of the vertex of the curve with equation
a) f(x + 7)
b) f(-x)
I’m
Answer:
We have to use the formule to calculate the vertex which is: V(-b/2a;4ac-b^2/4a)
A) y=x+7 where a=1 b=0 and c=7
By replacing we have: V(0;28/4) V(0;7)
B) y=-x where a=-1 b and c=0 so V(0,0)
This year a small business had a total of $35,100.If this is 35% more than their total revenue the previous year, what was their total revenue the previous year
Answer:
22,815
Step-by-step explanation:
35% of 35,100 is 12285, then you subtract that from 35,100 to get 22,815. Hope this helps.
A circle has a circumference of 3.14 units.
What is the diameter of the circle?
inits
Answer:
D = 1
Step-by-step explanation:
0.99949
round the answer so its 1
diameter = 1
Hi, I am very stuck on questions 17 and 18. Can someone help please? Thanks
9514 1404 393
Answer:
17) x = 10√2
18) x = 4√6
Step-by-step explanation:
These problems rely on your knowledge of the side ratios of special triangles
45°-45°-90° triangle: 1 : 1 : √2
30°-60°-90° triangle: 1 : √3 : 2
__
17) 5 is the short side of the isosceles right triangle, so its hypotenuse is 5√2. That length is the shortest side of the 30/60/90 triangle, so its longest side is 2 times that:
x = 10√2
__
18) 8 is the longest side of the 30/60/90 triangle, so its long leg will be 8(√3)/2 = 4√3. The hypotenuse of the isosceles right triangle is √2 times that, so ...
x = (4√3)(√2)
x = 4√6
Multiply (3x-5)(x+4)
Answer:
3x^2+7x-20
Step-by-step explanation:
Answer:
expand the brackets
3x^2 + 7x -20
Step-by-step explanation:
(3x-5)(x+4)
= 3x^2 + 12x - 5x + 20
= 3x^2 + 7x + 20
(12 + 31). Find the midpoint m of 21 (8 + 5i) and 22 Express your answer in rectangular form.
The average test score for 8 students is 5 the scores for 7 of the 8 students are shown what is the score of the 8th student
Answer:
70
Step-by-step explanation
Find the diagram attached
Average = Sum of scores/sample size
Given the 7 numbers
20, 20, 20, 30, 80, 80, 80
Average = 50
5 = 20+20+20+30+80+80+80+x/8
x is the score of the 8th student
50 = 330+x/8
400 = 330+x
x = 400-330
x = 70
Hence the score of the 8th student is 70
some pls help I have a couple min left plzz
find f(4) if f(x) = x - 6
Please help.
Is algebra.
Answer:
Step-by-step explanation:
a solution is where both of the lines meet. or they have the same point on each line. so you can set the equation of each line equal to the other.
for this "solution" just look at the graph and see where the two lines meet.. and find the x coordinate of that point.
I see it meeting at x =2 get it?
Harpo, Groucho, Chico, Zeppo, Gummo, Karl, and Skid have won three tickets to the opera. They will randomly choose three people from their group to attend the opera. How many outcomes are possible?
Answer:
35
Step-by-step explanation:
This is a combination problem therefore we need to use the combination formula using factorials, plug in the values for n and r which would be 7 since there are 7 individuals in the group and 3 because we are making outcomes of 3.
C(n,r)=C(7,3)
=7!(3!(7−3)!)
=7!3!×4!
= 35
Finally, we can see that the total number of possible outcomes is 35
Use the equation y=2x-5
To find y when x=3z
Answer:
If y = 2x - 5, and x = 3z, then y = 6z - 5
Find the angle between the given vectors to the nearest tenth of a degree.
u = <-5, 8>, v = <-4, 8>
2.7°
-7.3°
5.4°
15.4°
9514 1404 393
Answer:
(c) 5.4°
Step-by-step explanation:
We can simply determine the difference between the angles of the vectors:
arctan(8/-5) -arctan(8/-4) = 122.005° -116.565° = 5.440°
The angle between the vectors is about 5.4°.
__
Alternate solutions
1) We could also determine the angle of their ratio.
u/v = (-5 +8i)/(-4 +8i) = (-5 +8i)(-4 -8i)/(4² +8²) = (84 +8i)/80 = 1.05 +0.1i
angle = arctan(0.1/1.05) = 5.440°
__
2) Tan(a-b) = (tan(a)+tan(b))/(1 -tan(a)(tan(b))
tan(∠u -∠v) = ((tan(∠u) -tan(∠v))/(1 +tan(∠u)tan(∠v))
= (-1.6 -(-2))/(1 +(-1.6)(-2)) = 0.4/4.2
∠u -∠v = arctan(2/21) = 5.440°
−|−37| = 37 true or false
Answer:
false
Step-by-step explanation:
The value of |−37| is 37
however, since the negative sign is in front of the absolute value,
−|−37| = -37
Therefore,
−|−37| does not equal 37
The given statement −|−37| = 37 is false.
Given that, −|−37| = 37.
We need to whether the given statement is true or false.
What is an absolute value?The absolute value of a variable x is represented by |x| which is pronounced as 'Mod x' or 'Modulus of x'. 'Modulus' is a Latin word, which means 'measure'. Absolute value is commonly referred to as numeric value or magnitude. The absolute value represents only the numeric value and does not include the sign of the numeric value. The modulus of any vector quantity is always taken as positive and is its absolute value.
Now, |−37|=37
So, -|−37|=-37
Therefore, the given statement is false.
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Please help with these (algebra)